Matrix-vector multiplication is one of the most commonly used mathematical operations in science and engineering computations. Mathematically, a matrix is usually represented by a two-dimensional array of real numbers, and a vector is represented by a one-dimensional array of real numbers. Since a matrix can be viewed as an array of vectors, the matrix-vector multiplication operation can be generalized to vector-vector multiplication (inner product) or matrix-matrix multiplication operations. In today's computer systems, matrix-vector multiplication operations are performed by digital integrated circuits, in which the numbers are represented in binary format and the computation is performed by Boolean logic circuits.
The existence of resistive memory devices, such as the memristor, resistive random-access memory (RRAM), and spintronic switches, were predicted in circuit theory nearly forty years ago. However, it wasn't until 2008 that the first physical realization was demonstrated by HP Labs through a TiO2 thin-film structure. Afterward, many resistive memory materials and devices have been reported or rediscovered. The resistive memory device has many promising features, such as non-volatility, low-power consumption, high integration density, and excellent scalability. More importantly, the unique property to record the historical profile of the excitations on the device makes it an ideal candidate to perform storage and computation functions in one device.
For the purpose of succinct description, the present invention uses the terminology “memristor” to represent the category of “resistive memory device”. For the remainder of the patent description, references to “memristor” shall be regarded as referring to any “resistive memory device”.
Based on circuit theory, an ideal memristor with memristance M builds the relationship between the magnetic flux φ and electric charge q that passes through the device, that is, dφ=M·dq. Since the magnetic flux and the electric charge are time dependent parameters, the instantaneous memristance varies with time and reflects the historical profile of the excitations through the device.
When developing actual memristive devices, many materials have demonstrated memristive behavior in theory and/or experimentation via different mechanisms. In general, a certain energy (or threshold voltage) is required to enable a state change in a memristor. When the electrical excitation through a memristor is greater than the threshold voltage, e.g., |vin|>|vth|, the memristance changes. Otherwise, the memristor behaves like a resistor.